Wavelet analysis residual kriging vs. neural network residual kriging

This paper deals with the problem of spatial data mapping. A new method based on wavelet interpolation and geostatistical prediction (kriging) is proposed. The method - wavelet analysis residual kriging (WARK) - is developed in order to assess the problems rising for highly variable data in presence of spatial trends. In these cases stationary prediction models have very limited application. Wavelet analysis is used to model large-scale structures and kriging of the remaining residuals focuses on small-scale peculiarities. WARK is able to model spatial pattern which features multiscale structure. In the present work WARK is applied to the rainfall data and the results of validation are compared with the ones obtained from neural network residual kriging (NNRK). NNRK is also a residual-based method, which uses artificial neural network to model large-scale non-linear trends. The comparison of the results demonstrates the high quality performance of WARK in predicting hot spots, reproducing global statistical characteristics of the distribution and spatial correlation structure.

Source wavelet estimation for waveform inversion of crosshole georadar data

AbstractFor a wide range of environmental, hydrological, and engineering applications there is a fast growing need for high-resolution imaging. In this context, waveform tomographic imaging of crosshole georadar data is a powerful method able to provide images of pertinent electrical properties in near-surface environments with unprecedented spatial resolution. In contrast, conventional ray-based tomographic methods, which consider only a very limited part of the recorded signal (first-arrival traveltimes and maximum first-cycle amplitudes), suffer from inherent limitations in resolution and may prove to be inadequate in complex environments. For a typical crosshole georadar survey the potential improvement in resolution when using waveform-based approaches instead of ray-based approaches is in the range of one order-of- magnitude. Moreover, the spatial resolution of waveform-based inversions is comparable to that of common logging methods. While in exploration seismology waveform tomographic imaging has become well established over the past two decades, it is comparably still underdeveloped in the georadar domain despite corresponding needs. Recently, different groups have presented finite-difference time-domain waveform inversion schemes for crosshole georadar data, which are adaptations and extensions of Tarantola's seminal nonlinear generalized least-squares approach developed for the seismic case. First applications of these new crosshole georadar waveform inversion schemes on synthetic and field data have shown promising results. However, there is little known about the limits and performance of such schemes in complex environments. To this end, the general motivation of my thesis is the evaluation of the robustness and limitations of waveform inversion algorithms for crosshole georadar data in order to apply such schemes to a wide range of real world problems.One crucial issue to making applicable and effective any waveform scheme to real-world crosshole georadar problems is the accurate estimation of the source wavelet, which is unknown in reality. Waveform inversion schemes for crosshole georadar data require forward simulations of the wavefield in order to iteratively solve the inverse problem. Therefore, accurate knowledge of the source wavelet is critically important for successful application of such schemes. Relatively small differences in the estimated source wavelet shape can lead to large differences in the resulting tomograms. In the first part of my thesis, I explore the viability and robustness of a relatively simple iterative deconvolution technique that incorporates the estimation of the source wavelet into the waveform inversion procedure rather than adding additional model parameters into the inversion problem. Extensive tests indicate that this source wavelet estimation technique is simple yet effective, and is able to provide remarkably accurate and robust estimates of the source wavelet in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity as well as significant ambient noise in the recorded data. Furthermore, our tests also indicate that the approach is insensitive to the phase characteristics of the starting wavelet, which is not the case when directly incorporating the wavelet estimation into the inverse problem.Another critical issue with crosshole georadar waveform inversion schemes which clearly needs to be investigated is the consequence of the common assumption of frequency- independent electromagnetic constitutive parameters. This is crucial since in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behaviour. In particular, in the presence of water, there is a wide body of evidence showing that the dielectric permittivity can be significantly frequency dependent over the GPR frequency range, due to a variety of relaxation processes. The second part of my thesis is therefore dedicated to the evaluation of the reconstruction limits of a non-dispersive crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. I show that the inversion algorithm, combined with the iterative deconvolution-based source wavelet estimation procedure that is partially able to account for the frequency-dependent effects through an "effective" wavelet, performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

Waveform inversion of crosshole georadar data: influence of source wavelet variability and the suitability of a single wavelet assumption

Waveform-based tomographic imaging of crosshole georadar data is a powerful method to investigate the shallow subsurface because of its ability to provide images of electrical properties in near-surface environments with unprecedented spatial resolution. A critical issue with waveform inversion is the a priori unknown source signal. Indeed, the estimation of the source pulse is notoriously difficult but essential for the effective application of this method. Here, we explore the viability and robustness of a recently proposed deconvolution-based procedure to estimate the source pulse during waveform inversion of crosshole georadar data, where changes in wavelet shape with location as a result of varying near-field conditions and differences in antenna coupling may be significant. Specifically, we examine whether a single, average estimated source current function can adequately represent the pulses radiated at all transmitter locations during a crosshole georadar survey, or whether a separate source wavelet estimation should be performed for each transmitter gather. Tests with synthetic and field data indicate that remarkably good tomographic reconstructions can be obtained using a single estimated source pulse when moderate to strong variability exists in the true source signal with antenna location. Only in the case of very strong variability in the true source pulse are tomographic reconstructions clearly improved by estimating a different source wavelet for each transmitter location.

Analysis of an iterative deconvolution approach for estimating the source wavelet during waveform inversion of crosshole ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole georadar data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a time-domain waveform inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little-to-no trade-off between the wavelet estimation and the tomographic imaging procedures.

Source-wavelet estimation during full-waveform inversion of ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole ground-penetrating radar (GPR) data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a recently published time-domain inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity of both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little to no trade-off between the wavelet estimation and the tomographic imaging procedures.

Evaluation of the reconstruction limits of a frequency-independent crosshole georadar waveform inversion scheme in the presence of dispersion

Waveform tomographic imaging of crosshole georadar data is a powerful method to investigate the shallow subsurface because of its ability to provide images of pertinent petrophysical parameters with extremely high spatial resolution. All current crosshole georadar waveform inversion strategies are based on the assumption of frequency-independent electromagnetic constitutive parameters. However, in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behavior. In this paper, we evaluate synthetically the reconstruction limits of a recently published crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. Our results indicate that, when combined with a source wavelet estimation procedure that provides a means of partially accounting for the frequency-dependent effects through an "effective" wavelet, the inversion algorithm performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

Enhancing the vertical resolution of surface georadar data

There are far-reaching conceptual similarities between bi-static surface georadar and post-stack, "zero-offset" seismic reflection data, which is expressed in largely identical processing flows. One important difference is, however, that standard deconvolution algorithms routinely used to enhance the vertical resolution of seismic data are notoriously problematic or even detrimental to the overall signal quality when applied to surface georadar data. We have explored various options for alleviating this problem and have tested them on a geologically well-constrained surface georadar dataset. Standard stochastic and direct deterministic deconvolution approaches proved to be largely unsatisfactory. While least-squares-type deterministic deconvolution showed some promise, the inherent uncertainties involved in estimating the source wavelet introduced some artificial "ringiness". In contrast, we found spectral balancing approaches to be effective, practical and robust means for enhancing the vertical resolution of surface georadar data, particularly, but not exclusively, in the uppermost part of the georadar section, which is notoriously plagued by the interference of the direct air- and groundwaves. For the data considered in this study, it can be argued that band-limited spectral blueing may provide somewhat better results than standard band-limited spectral whitening, particularly in the uppermost part of the section affected by the interference of the air- and groundwaves. Interestingly, this finding is consistent with the fact that the amplitude spectrum resulting from least-squares-type deterministic deconvolution is characterized by a systematic enhancement of higher frequencies at the expense of lower frequencies and hence is blue rather than white. It is also consistent with increasing evidence that spectral "blueness" is a seemingly universal, albeit enigmatic, property of the distribution of reflection coefficients in the Earth. Our results therefore indicate that spectral balancing techniques in general and spectral blueing in particular represent simple, yet effective means of enhancing the vertical resolution of surface georadar data and, in many cases, could turn out to be a preferable alternative to standard deconvolution approaches.

Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

Middle and Late Jurassic carbon stable-isotope stratigraphy and radiolarite sedimentation of the Umbria-Marche basin (Central Italy)

A continuous carbon isotope curve from Middle-Upper Jurassic pelagic carbonate rocks was acquired from two sections in the southern part of the Umbria-Marche Apennines in central Italy. At the Colle Bertone section (Terni) and the Terminilletto section (Rieti), the Upper Toarcian to Bajocian Calcari e Marne a Posidonia Formation and the Aalenian to Kimmeridgian Calcari e Marne a Posidonia and Calcari Diasprigni formations were sampled, respectively. Biostratigraphy in both sections is based on rich assemblages of calcareous nannofossils and radiolarians, as well as some ammonites found in the upper Toarcian-Bajocian interval. Both sections revealed a relative minimum of delta(13)C(PDB) close to + 2 parts per thousand in the Aalenian and a maximum around 3.5 parts per thousand in early Bajocian, associated with an increase in visible chert. In basinal sections in Umbria-Marche, this interval includes the very cherry base of the Calcari Diasprigni Formation (e.g. at Valdorbia) or the chert-rich uppermost portion of the Calcari a Posidonia (e.g at Bosso). In the Terminilletto section, the Bajocian-early Barthonian interval shows a gradual decrease in delta(13)C(PDB) values and a low around 2.3 parts per thousand. This part of the section is characterised by more than 40 m of almost chart-free limestones and correlates with a recurrence of limestone-rich facies in basinal sections at Valdorbia. A double peak with values of delta(13)C(PDB) around + 3 parts per thousand was observed in the Callovian and Oxfordian, constrained by well preserved radiolarian faunas. The maxima lie in the Callovian and the middle Oxfordian, and the minimum between the two peaks should be near the Callovian/Oxfordian boundary. In the Terminilletto section, visible chert increases together with delta(13)C(PDB) values from the middle Bathonian and reaches peak values in the Callovian-Oxfordian. In basinal sections in Umbria-Marche, a sharp increase in visible chert is observed at this level within the Calcari Diasprigni. A drop of delta(13)C values towards + 2 parts per thousand occurs in the Kimmeridgian and coincides with a decrease of visible chert in outcrop. The observed delta(13)C positive anomalies during the early Bajocian and the Callovian-Oxfordian may record changes in global climate towards warmer, more humid periods characterised by increased nutrient mobilisation and increased carbon burial. High biosiliceous (radiolarians, siliceous sponges) productivity and preservation appear to coincide with the delta(13)C positive anomalies, when the production of platform carbonates was subdued and ceased in many areas, with a drastic reduction of periplatform ooze input in many Tethyan basins. The carbon and silica cycles appear to be linked through global warming and increased continental weathering. Hydrothermal events related to extensive rifting and/or accelerated oceanic spreading may be the endogenic driving force that created a perturbation of the exogenic system (excess CO2 into the atmosphere and greenhouse conditions) reflected by the positive delta(13)C shifts and biosiliceous episodes.

Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging.

Methods are presented to map complex fiber architectures in tissues by imaging the 3D spectra of tissue water diffusion with MR. First, theoretical considerations show why and under what conditions diffusion contrast is positive. Using this result, spin displacement spectra that are conventionally phase-encoded can be accurately reconstructed by a Fourier transform of the measured signal's modulus. Second, studies of in vitro and in vivo samples demonstrate correspondence between the orientational maxima of the diffusion spectrum and those of the fiber orientation density at each location. In specimens with complex muscular tissue, such as the tongue, diffusion spectrum images show characteristic local heterogeneities of fiber architectures, including angular dispersion and intersection. Cerebral diffusion spectra acquired in normal human subjects resolve known white matter tracts and tract intersections. Finally, the relation between the presented model-free imaging technique and other available diffusion MRI schemes is discussed.

Multi-parametric evaluation of sit-to-stand and stand-to-sit transitions in elderly people.

The aim of this study was to extract multi-parametric measures characterizing different features of sit-to-stand (Si-St) and stand-to-sit (St-Si) transitions in older persons, using a single inertial sensor attached to the chest. Investigated parameters were transition's duration, range of trunk tilt, smoothness of transition pattern assessed by its fractal dimension, and trunk movement's dynamic described by local wavelet energy. A measurement protocol with a Si-St followed by a St-Si postural transition was performed by two groups of participants: the first group (N=79) included Frail Elderly subjects admitted to a post-acute rehabilitation facility and the second group (N=27) were healthy community-dwelling elderly persons. Subjects were also evaluated with Tinetti's POMA scale. Compared to Healthy Elderly persons, frail group at baseline had significantly longer Si-St (3.85±1.04 vs. 2.60±0.32, p=0.001) and St-Si (4.08±1.21 vs. 2.81±0.36, p=0.001) transition's duration. Frail older persons also had significantly decreased smoothness of Si-St transition pattern (1.36±0.07 vs. 1.21±0.05, p=0.001) and dynamic of trunk movement. Measurements after three weeks of rehabilitation in frail older persons showed that smoothness of transition pattern had the highest improvement effect size (0.4) and discriminative performance. These results demonstrate the potential interest of such parameters to distinguish older subjects with different functional and health conditions.